The language I'm working on has a verb-initial word order in basic sentences. It also has case marking for animate nouns, so I can move the word order around to express other things like topicalization and focus (also definitness, since I don't want an article) , but I'm not sure how.
My first thought was that putting any NP before the verb would make it the topic, which seemed pretty obvious, but then I realized most of the examples I've seen of this kind of thing were from more head-final languages. So my questions are:
1. How widespread is the rule that old information tends to appear first? Can I make it work with my word order? Is it better to switch things around and make the beginning of the sentence a focus position?

2. Wikipedia has an example, from my native language no less, that confused me even more:

In modern Hebrew, a topic may be adjoined to a sentence from the right-hand side, while the syntactic subject of the sentence is an expletive. (Note that "to the right" refers to the phrase's location in the standard linguistic representation of the sentence – left-to-right, Roman Alphabet – and is independent of the directionality of the given language's native script; hence the topic phrase is said to appear to the right, even though in Hebrew writing it is seen on the left.) For example, זה מאד מענין הספר הזה "ze meod meanyen ha-sefer ha-ze" (lit. "This is very interesting this book") means "This book is very interesting". The syntactic subject is "ze", which is meaningless, while the topic is "ha-sefer ha-ze" ("this book"), which appears to the right of (i.e. after the main clause of) the sentence, and not in its canonical subject position (which is occupied by the meaningless "ze").

Is that actually a topic, or should it be called something else? I saw the term "anti-topic" somewhere, is it the same thing?

3. I also planned to have a focus particle, but I don't know enough about about these. Does anyone know examples of languages that use one, or have ideas where to look?

Terminology of information structure is very messy and (nearly) same things are called by different terms and same terms are used for (nearly) same concepts.
Basically "topic" can either refer to a "meaning" entity of a referent mentioned before in the discourse or other ways derivable from it, or an entity known from the context of the speech partners. Or it can be a "form" entity that encodes the thing mentioned before - in "normal" sentences or somehow emphasized sentences.

Topic refers to the old shared information and functions as a reference point in the sentence so that the new information is given in respect to it. It's pretty common amongst languages that this old information appears quite early in the sentence and is followed by most of the new information. Intuitively this makes it easier for the audience to keep track of the discourse and link the news to the already established information. On the other hand, afterthough topics located at the end of the sentence, as in the Hebrew example, are also a thing that appears and I'll have to do more reading to understand them better.

Another common pattern is to move whatever strongly contrasting element in a sentence to its beginning, be it focus (new information) or topic (old information). This is what people usually think of when they write about "emphasis" in the grammar. These are typically more marked than your normal topics and foci that simply track what's old and what's new in the discourse and are likely places to see things like clefts of focus particles.

If your basic word order is verb-initial, I'd put the regular focus position following the verb. If you were to put the topic position at the start of the sentence before the verb, most of your sentences would then start with this topic and it wouldn't make much sense to call the word order verb-initial any more. You can still freely allow contrastive elements at the start of the sentence while keeping the basic word order verb-initial, since most sentences don't have these.

If your language explicitly recognizes topics as a grammatical element, I.e. it is a topic-prominent language, then VSO would only work if you allow the topic to come before the verb in order to ensure the topic and comment are sequential rather than nested, since having the topic nested within the comment would not make much sense.

This would still allow for VSO, as non-topic subjects and objects would still appear after the verb, e.g.

On the other hand, afterthough topics located at the end of the sentence, as in the Hebrew example, are also a thing that appears and I'll have to do more reading to understand them better.

This is very common in Japanese speech, not only for topics but pretty much anything, though it's technically not grammatically correct. I think one of the reasons is because Japanese is so apt to drop arguments, so you can easily put the verb in and end your clause prematurely, so people then realize what they said I is not clear, and they will add information. I also think it can sort of act as another type of focus shifting independent of the topic-comment structure, sort of like topicalizing the verb.

It might help you to know that, although there is a tradition of using "as for" to explain topics in linguistics, in normal English it's more common to use "now the X, ...", "regarding the X, ..." or just a plain "the X, it..." as topic constructions. Now focus, that is a more complex matter in English. ~ Focus, however, that is a more complex matter in English.

Mandarin Chinese is an example of a language that has a focus marker, namely 是 shi4 (placed before the focused constituent), accompanied by the particle 的 de later in the sentence.

You typically see this focus particle applied to adverbial adjuncts (of place or time) before the main verb or to the main verb itself, but you can apply it to subjects too:

是我们不希望发生任何事情的。
shi4 wo3men bu4 xi1wang4 fa1sheng1 ren4he2 shi4qing de
SHI 1P not wish happen any thing DE
'We don't want any of this to happen.' ~ 'It is us who don't want any of this to happen.'

Focus in English is generally handled with a number of strategies like intonation / emphatic pronunciation, moving constituents to the end of the sentence in the case of time and manner adverbials, using the passive voice (to move an agent to the end of the sentence, which is more amenable for focusing: The patient was murdered by his own doctor!), clefting...

If your language explicitly recognizes topics as a grammatical element, I.e. it is a topic-prominent language, then VSO would only work if you allow the topic to come before the verb in order to ensure the topic and comment are sequential rather than nested, since having the topic nested within the comment would not make much sense.

A key issue here is what should we understand "recognising topics as grammatical elements" to mean. I'm not sure that your statement can be extended to cover all languages, especially when the main strategies for topicalisation include word order or grammatical voices instead of explicit nominal topic marking. On the other hand, I have to admit that I can't remember reading much at all about information structure in VSO word order languages. I've seen some papers on Salish information structure, so I might need to read those carefully after Christmas. I also think that this thread could use some Philippine input.

However, I can think of some English sentences where the topical and focal elements aren't absolutely sequential, though there's no simple dedicated morphology for labelling either of them. Think for example the following question-answer pair,

How can I help you?It's that car of yours, that you could drive off from blocking my way.

The most topical element in the answer is the subject you since it refers to participant established in the previous sentence. Both the cleft in front of it and the rest of the sentence following it contain new information that's not been invoked before, meaning that the topic is surrounded on both sides by more focal elements (the cleft containing the emphasised part of the focus). It's also possible to construct sentences that have topical elements surrounding focal ones by using afterthoughts,

This book is interesting.
>It's interesting, this book.

In both of these cases the subject is the topic and the predicate the focus. The second sentence moves the lexical content of the subject into an afterthought while still retaining a pronominal dummy subject in the subject position. They refer to the same entity, this book, and are thus both topical. The result is a sentence where the focal part if surrounded by morphological elements corresponding to the topic. These examples may have their flaws if you dig deeper, but I think that they still demonstrate that requiring topics and foci to always be sequential is also too simplistic to pass as a universal rule.

A key issue here is what should we understand "recognising topics as grammatical elements" to mean. I'm not sure that your statement can be extended to cover all languages, especially when the main strategies for topicalisation include word order or grammatical voices instead of explicit nominal topic marking.

I was specifically referencing topic-prominent languages, where there are explicit, unobtrusive, and frequent strategies for marking topics and separating them from the comment, so it was not meant to cover all languages.

However, I can think of some English sentences where the topical and focal elements aren't absolutely sequential, though there's no simple dedicated morphology for labelling either of them. Think for example the following question-answer pair,

How can I help you?It's that car of yours, that you could drive off from blocking my way.

The most topical element in the answer is the subject you since it refers to participant established in the previous sentence. Both the cleft in front of it and the rest of the sentence following it contain new information that's not been invoked before, meaning that the topic is surrounded on both sides by more focal elements (the cleft containing the emphasised part of the focus).

I'm sorry, but this sentence is rather bizarre to me and I can't quite understand it. Indeed, "you" is old information, but (at least from the perspective of a topic-prominent language like Japanese), it is not the topic of that sentence; the topic is the car, (I'm talking about your car, here's information about it) and it was introduced at the beginning, as one would expect. I'm not sure about this example sentence though, so I may be misinterpreting you.

It's also possible to construct sentences that have topical elements surrounding focal ones by using afterthoughts,

This book is interesting.
>It's interesting, this book.

In both of these cases the subject is the topic and the predicate the focus. The second sentence moves the lexical content of the subject into an afterthought while still retaining a pronominal dummy subject in the subject position. They refer to the same entity, this book, and are thus both topical. The result is a sentence where the focal part if surrounded by morphological elements corresponding to the topic. These examples may have their flaws if you dig deeper, but I think that they still demonstrate that requiring topics and foci to always be sequential is also too simplistic to pass as a universal rule.

In this sentence, both "it" and "this book" have the same referent, so strictly speaking, the comment "is interesting" is not nested in the topic; rather, it is surrounded by two independent references to the topic. When I said, "having the topic nested within the comment would not make much sense," I meant having it nested within a single reference. A better example of what I meant would be something like:

*Learning is fun to ski.

This sentence does not work because I have inserted the comment "is fun" in the middle of a single reference to the topic "learning to ski" splitting it apart confusingly. This is the problem with having a topic-prominent VSO word order but forcing the verb to appear first. The reverse of this sentence would occur, where the comment is split in half by the topic:

Broke John the vase.

Naturally, if we're not talking about a strongly topic-prominent language, and this is just a matter of fronting, then this sort of construction should be fine, I think.

Another common pattern is to move whatever strongly contrasting element in a sentence to its beginning, be it focus (new information) or topic (old information). This is what people usually think of when they write about "emphasis" in the grammar. These are typically more marked than your normal topics and foci that simply track what's old and what's new in the discourse and are likely places to see things like clefts of focus particles.

This is more or less what I was thinking - not making the language topic-prominent, but allow elements to come before the verb to signal they're somehow important.

If your basic word order is verb-initial, I'd put the regular focus position following the verb. If you were to put the topic position at the start of the sentence before the verb, most of your sentences would then start with this topic and it wouldn't make much sense to call the word order verb-initial any more. You can still freely allow contrastive elements at the start of the sentence while keeping the basic word order verb-initial, since most sentences don't have these.

What does a "regular focus position" mean? Wouldn't that be just the basic word order?
If I go by your idea, then for this "unmarked" sentence:
ludj cesu liimii.
eat.IMPF.3SG bird.NOM fish-SG.ACC
The bird is eating the fish.

Is the focus here on "bird" or on "eating"? (Predicate-focus or argument-focus?)

If your language explicitly recognizes topics as a grammatical element, I.e. it is a topic-prominent language, then VSO would only work if you allow the topic to come before the verb in order to ensure the topic and comment are sequential rather than nested, since having the topic nested within the comment would not make much sense.

How can one tell if topic is a grammatical element or not?

This is very common in Japanese speech, not only for topics but pretty much anything, though it's technically not grammatically correct. I think one of the reasons is because Japanese is so apt to drop arguments, so you can easily put the verb in and end your clause prematurely, so people then realize what they said I is not clear, and they will add information. I also think it can sort of act as another type of focus shifting independent of the topic-comment structure, sort of like topicalizing the verb.

Naturally, if we're not talking about a strongly topic-prominent language, and this is just a matter of fronting, then this sort of construction should be fine, I think.

Yeah, I'm arguably talking about information structure in languages in general. In most languages topic is mostly a mental label of established "aboutness" and even when it does have dedicated morphology associated with it, it's nowhere near as singled out from the rest of the sentence as in Japanese.

What I still find a bit baffling is the relation of VSO syntax and the demand to keep the topic and focus strictly sequential. By far the most common sentence type information structure wise is subject-topic and predicate-focus. If you can't allow the topical S to come between focal V and O, wouldn't this mean that the VSO order is not the most common word order in the actual usage of the language? The fact that we still see a good number of VSO languages means that either the rule of strict sequentiality is not universal or that these languages aren't classified as being VSO based on their most typical word order.

What does a "regular focus position" mean? Wouldn't that be just the basic word order?
If I go by your idea, then for this "unmarked" sentence:
ludj cesu liimii.
eat.IMPF.3SG bird.NOM fish-SG.ACC
The bird is eating the fish.

Is the focus here on "bird" or on "eating"? (Predicate-focus or argument-focus?)

By the regular focus position I mean the place where the new information content of the sentence is most likely to be located. This doesn't have to have any formal rule associated with it, but often you'll find that new information is more likely to be located in certain parts of the sentence than in others.

The subject "the bird" in the sentence

The bird is eating fish.

is a definite noun (and thus already established information) and the rest of the sentence is providing new information in relation to it. Thus the most likely scenario is that the bird is the topic of the sentence and the rest of the sentence is in focus,

The bird [is eating fish]FOC.

This case is called "predicate focus" since the full predicate, including the object, is in focus with no part of it singled out as being more central than the others. You are simply telling what the subject is doing, maybe as an answer to the question "What is the bird doing?"

The focus can also be narrowed to individual elements like the verb

The bird [is eating]FOC the fish.

or the object

The bird is eating [fish]FOC.

In English the main difference between these is that the strongest stress falls on the focal elements when speaking and it's thus located on different words. Another difference is that if you want to remove the object from being focal, and thus make it more topical, it's going to have to be information that's already shared to some extent. This means that it's most natural to mark it definite in English.

Finding out what is the focus of the sentence is easiest if you think what question the sentence would be an answer to. The verb-focus sentence could be an answer to the question "What is the bird doing with the fish?" and the object-focus sentence to the question "What is the bird eating?" The object-focus sentence can be further altered by making the focus contrastive and fronting it into a cleft,

[It's fish]FOC that the bird is eating.

This has the same information flow as the previous sentence but it gives a signal that the focus is now contrasted with some previous presupposition. Something like this could be said in response to a question like "Is it mussels that the bird is eating?"

A big difficulty in understanding these concepts is that they don't necessarily have so clear cut borders with each other. What I rather see is a spectrum ranging from topical elements to focal elements with different gradations of old and new inforamation in between. It's also important to notice that different languages do grammatical marking of topic and focus in their own ways and what the grammar of a language recognises as a marked topic or focus usually doesn't have a one to one correspondence to the underlying information structure notions. There are furthermore related factors of contrastiveness and foregrounding or backgrounding which play their role in the information flow of discourse and have a pretty complex relation with topic and focus.

I don't have any specific thesis to expound here, but I wanted to pick up on a few points while I think of them.

- one reason it's easy to get confused about old/new information is that it's often explained in terms of emphasis, which is really something entirely different. Though still, I guess, a part of the information structure.

Focused (new) elements are typically emphasised. But topics can be too, particularly when the topic is being introduced or rapidly changed. For instance:

It's fish, that the bird eats. - OK, emphasised focus. Context: what does the bird eat?Fish, the bird eats; mice, the cat - But here, almost identical procedures (fronting, phonological emphasis) are used to produce emphasised topics instead. [Similarly, "as for fish, the bird eats it", "fish is eaten by the bird", etc]. Context: what happens to fish in your house?

Because English not only lacks a simple syntactic mechanism for showing either emphasis or focus, but uses very similar mechanisms for both, it's easy for English speakers to get very confused.

- there can be several bits of focused information. And there can be several bits of topical information. Topics can be nested. Now on Tuesdays, fish gets given to the cat - this is 'about' fish, but it's also, at a higher level 'about' what happens on Tuesdays. Either or both can be detopicalised: As for the cat, it's on Tuesdays that it gets given fish (both detopicalised); Now on Tuesdays, the cat gets given fish (Tuesdays still topical; fish no longer so); Fish gets given to the cat on the Tuesday (Fish still topical, Tuesdays no longer so).

More generally, every time a sentence has multiple definite nouns in it, it has multiple topicalised bits of information. While some language pick out a single grammatical Topic, in languages that don't do this "topic" is a bit more a continuum than a binary thing, and it's something that interacts with emphasis.

- topic isn't really something that works at the clause level. I mean, it can do ("The car - it's sinking!"). But it's usually more about structuring the attention and understanding of the listener throughout the whole of a discourse. Topicalisation in one clause may be made clear by the contents of a preceding clause (The dog bit a cat; the mouse was then eaten by the cat - on the surface it looks like 'the mouse' is the topic of the second clause, but the context of the first clause suggests the cat is probably more topical than the mouse (though because it's definite it must be at least partly topical) (the focus is probably the verb)), and the topicalisation in one clause may be chosen less because of the information in that clause and more from a desire to set up a topic for predicted future clauses (that last example might be more elegant as A cat was bitten by the dog, and it then ate the mouse, even though in the first clause ordinarily the definite and agentive dog would be a better candidate for topicalisation than the indefinite and patientive cat).

- topic is related to subject. Subjects are typically topics. In languages without much 'official' syntax to show topichood, voice may be used to use subject to help clarify topic. Also, note that both topic and subject can be used to link related clauses (which is one reason it helps to make them be the same things).

- topic is likewise related to definiteness.

- since definiteness and subjecthood are related to voice, transitivity and valence... so is topic. A change in topic can be signalled by a change in transitivity and/or valence - for instance, many Austronesian languages require the patient of a transitive verb to be definite, so making the verb intransitive can imply indefiniteness, which can be used to dis-imply topichood. So we might have, say: Bridge crushed children (transitive, so the children are definite, so they're probably the topic), vs Bridge fell, crushing children (intransitive, so the children are probably indefinite and cannot be the topic, so the bridge probably is). Concerns like this around information structure seem to be a big part of what motivations the various austronesian hijinks with voice and transitivity.

- topic can also be related to categories like mirativity on the verb, and to animacy hierarchies.